How to forward traffic between a tun device and a tap device?

I have an application that creates a tun device (think a VPN), and I've set up a tap device on the same host that's connected to a bridge (OVS, actually). What I'd like to do is have all traffic from that tun interface "route" through the tap device. I'm using quotes here because I know that since routing is an L3 operation I can't actually route the traffic into the tap interface.

Is it possible to achieve this without just making that tap device a tun device and just routing the traffic?

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